Dimensional fragility of the Kardar-Parisi-Zhang universality class

TL;DR

This paper investigates how the scaling behavior of models related to the KPZ universality class changes with substrate dimensionality, revealing a fragility that challenges the assumption of universal behavior across dimensions.

Contribution

It demonstrates that models with KPZ symmetries deviate from KPZ scaling as system dimension increases, highlighting limitations of universality in higher dimensions.

Findings

KPZ models show dimensional dependence in their asymptotic behavior

Deviations from KPZ scaling occur at higher dimensions

Universality principles may not fully apply across all dimensions

Abstract

We assess the dependence on substrate dimensionality of the asymptotic scaling behavior of a whole family of equations that feature the basic symmetries of the Kardar-Parisi-Zhang (KPZ) equation. Even for cases in which, as expected from universality arguments, these models display KPZ values for the critical exponents and limit distributions, their behavior deviates from KPZ scaling for increasing system dimensions. Such a fragility of KPZ universality contradicts naive expectations, and questions straightforward application of universality principles for the continuum description of experimental systems.